A special class of change-point models, where the change is defined as a shift of observations means, is considered. We show that such models can be transformed into a nonlinear regression problem. It is proven thatM-estimators can localize the change point, and at the same time, consistently estimate the unknown parameters characterizing the change behavior. For a special class of continuous models we prove an asymptotic normality ofM-estimators simultaneously estimating the change-point and the related parameters.